PhD Chapter 3
Results 1/3
This series of files compile all analyses done during Chapter 3:
- Section 1 presents the calculation of the indices of exposure.
- Section 2 presents variable exploration and regressions results.
- Section 3 presents species distribution models.
All analyses have been done with R 4.0.2.
Click on the table of contents in the left margin to assess a specific analysis.
Click on a figure to zoom it
Sources of activity considered for the analyses:
- aquaculture influence: AquaInf
- city influence: CityInf
- industries influence: InduInf
- dredging collecting zones: CollDred
- dredging dumping zones: DumpDred
- commercial ships mooring site: MoorShip
- commercial ships traffic routes: TrafShip
- rainwater sewers: RainSew
- wastewater sewers: WastSew
- city wharves: CityWha
- industries wharves: InduWha
Fisheries data considered for the analyses (expressed as number of fishing events or kilograms of collected individuals for each gear):
| Gear | Code | Years | Events | Species |
|---|---|---|---|---|
| Trap | TrapFish | 2010-2015 | 1061 | Buccinum sp., Cancer irroratus, Chionoecetes opilio, Homarus americanus |
| Bottom-trawl | TrawFish | 2013-2014 | 2 | Pandalus borealis |
| Net | NetFish | 2010 | 5 | Clupea harengus, Gadus morhua |
| Dredge | DredFish | 2010-2014 | 21 | Mactromeris polynyma |
1. Maps
1.1. General map
1.2. Parameters maps
Maps of abiotic habitat variables:
Depth
Slope
River CDOM
Maps of functional traits density:
Body: non-calcifying
Body: chitinous
Body: aragonite
Body: calcite
Body: calcareous
Size: small
Size: medium
Size: large
Food: grazers
Food: predators
Food: scavengers
Food: filter feeders
Food: surface deposit feeders
Food: subsurface deposit feeders
Food: parasites
Lifestyle: mobile
Lifestyle: sessile
Lifestyle: burrower
Lifestyle: crawler
Lifestyle: swimmer
Lifestyle: tubicolous
2. Modelling the influence of human activities
We computed an exposure index for each human activity, which we will use for regression models and SDM (see section 2). Two categories of exposure index were calculated seperately: one for land- and sea-based activities and one for fisheries. These indices are relative, with a variation between 0 (low exposure) to 1 (high exposure).
A cumulative exposure index has been calculated by adding index of exposure of each activity.
2.1. Individual indices of exposure
2.1.1. Land- and sea-based activities
The following map present the sources of land- and sea-based human activities considered here. For each activity, we calculated an index of exposure \(E_{ij}\).
Methodology
To calculate \(E_{ij}\), we considered the diffusion of theoretical particles in an ecosystem. These particles are the resultant of an activity, such as contaminants or sediment, and they difuse from the source of the activity. Three types of particles have been considered, in order to model a certain sinking rate. Their combination will allow to represent each activity by a unique signature.
- slow-sinking particles (previously < 4 µm): e.g. clay, dissolved organic matter, small bacteria, viruses, chemical components, proteins
- medium-sinking particles (previously between 4 µm and 2 mm): e.g. sand, silt, small particulate organic matter, large bacteria, phytoplankton, zooplankton
- fast-sinking particles (previously > 2 mm): e.g. gravel, large particulate organic matter, clusters of dead organisms, large zooplankton, larger organisms
We simulated the dispersion of these particles using the distance from the source and an inverse logarithm relationship, to account for a ‘journey’ in a 2D environment while reducing the contribution of highest values. A cutoff distance for each particle type was used to simulate sedimentation, thus establishing a threshold after which the exposure becomes negligible.
The general equation for \(E_{ij}\) is:
\[ \left\{\begin{matrix} E_{ij} = \frac{1}{ln(D_{ij} + 1)} & D_{ij} < T \\ E_{ij} = 0 & D_{ij} > T \end{matrix}\right. \]
- \(D_{ij}\) is the minimal distance from the source of activity
- \(T\) is the threshold defined by the cutoff distances of each particle type
- \(i\) is a station
- \(j\) is a human activity
Cutoff distance for \(T\) (in meters) has been initialized as such:
| slow | medium | fast | |
|---|---|---|---|
| cutoff | 7500 | 3500 | 500 |
⚠️ These values need to be groundtruthed by litterature research and expert opinion.
\(D_{ij}\) has been calculated with least-cost pathfinding methods from the package gdistance. To compute the trajectory of the particles of each class, we established a connectivity model based on a ‘resistance seascape’ concept. First, we created a raster considering our study area, whose cell can be selected to obtain the path connecting start (source of the activity) and end (raster cell) points. Each cell has a cost to be included in this path, which is defined on physical constraints to account for environmental behaviour. The length of the final path then gives the minimal distance.
We considered three underlying principles for the physical constraints:
- marine ecosystems: particles cannot disperse on land
- gravity: particles disperse easily from shallow to deeper depths, while the reverse is difficult
- hydrodynamism: particles disperse according to local hydrodynamical currents
Thus, the connectivity model considered: (i) coasts and islands as boundaries unselectable by the algorithm, (ii) bathymetry, (iii) river plumes as hydrodynamical fronts with an intensity and a direction (a complete circulation model in BSI is not yet available).
⚠️ For now, only the two first constraints are implemented.
These constraints are included the transition function \(f_{j}\), used by costDistance() when creating the least-cost path. It computes connectivity values from a cell to its eight closest neighbours (chess queen configuration), with these conditions:
- land is set with a connectivity of 0, so that corresponding cells cannot be chosen by the pathfinding algorithm
- bathymetry is compared between two cells:
- when point A is shallower than point B, connectivity is high
- when point A is deeper than point B, connectivity is low (with a certain diffusion)
- CDOM content (proxy of hydrodynamism) is compared between two cells (NOT IMPLEMENTED YET)
Values of the parameters used for bathymetry and hydrodynamism contraints depend on the types of particle:
- slow-sinking particles: influenced primarily by hydrodynamics and diffusing over extended areas; gravity eventually sinks them; easily resuspended
- medium-sinking particles: particles both sinking due to gravity and spreading by hydrodynamic influence, resuspension possible but difficult
- fast-sinking particles: dense aggregates that sink easily due to gravity and are unaffected by hydrodynamical effects; resuspension is highly difficult
The equation for \(D_{ij}\) is then:
\[ D_{ij} = \sum_{k}^{s,m,f} f_{k} \left( B_{i}, H_{i}, T_{k} \right) . p_{jk} \]
- \(f_{k}\) is the transition function
- \(B_{i}\) is the bathymetry constraint
- \(H_{i}\) is the hydrodynamics constraint
- \(T_{k}\) is the cutoff distance
- \(p_{jk}\) is the proportion of each type of particle
- \(i\) is a station
- \(j\) is a human activity
- \(k\) is the particle type (slow, medium, fast sinking)
With the transition functions \(f_{j}\):
| Particle type | Transition function |
|---|---|
| Slow | ifelse(bathy[1] > bathy[2], (1 - ((bathy[2] - bathy[1]) / bathy[2])), 0.9) |
| Medium | ifelse(bathy[1] > bathy[2], (1 - ((bathy[2] - bathy[1]) / bathy[2])), 0.45) |
| Fast | ifelse(bathy[1] > bathy[2], (1 - ((bathy[2] - bathy[1]) / bathy[2])), 0.1) |
And the proportion of each particule size \(p_{jk}\):
| AquaInf | CityInf | InduInf | CollDred | DumpDred | MoorShip | TrafShip | RainSew | WastSew | CityWha | InduWha | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| slow | 0.6 | 0.6 | 0.7 | 0.1 | 0.1 | 0.4 | 0.4 | 0.5 | 0.4 | 0.4 | 0.4 |
| medium | 0.3 | 0.3 | 0.2 | 0.3 | 0.3 | 0.4 | 0.4 | 0.4 | 0.5 | 0.4 | 0.4 |
| fast | 0.1 | 0.1 | 0.1 | 0.6 | 0.6 | 0.2 | 0.2 | 0.1 | 0.1 | 0.2 | 0.2 |
⚠️ These values need to be groundtruthed by litterature research and expert opinion.
The combination of each particule size uses a weighted addition, but different relationships may be tested in the future. Finally, \(E_{ij}\) have been standardized by the minimal and maximal values to allow comparisons.
Results
The following maps present the values of \(E_{ij}\) for land- and sea-based activities (grey = low exposure; dark blue = high exposure).
AquaInf
CityInf
InduInf
CollDred
DumpDred
MoorShip
TrafShip
RainSew
WastSew
CityWha
InduWha
2.1.2. Fisheries
These data belong to Department of Fisheries and Oceans Canada, with a permission granted to David Beauchesne. As such, we cannot present raw products and we will work on derived data.
Here, \(E_{ij}\) have been calculated with a proxy based on fisheries data for each gear used in the area.
Methodology
We extracted data from a global database for the St. Lawrence, for all fishing events occuring within the Baie des Sept-Îles. Four types of gears (traps, bottom-trawls, nets and dredges) have been considered in the bay between 2010 and 2015. Eight species have been gathered (see table at the top of this page).
As each gear was not used consistently during this period, we averaged the number of fishing events to obtain a proxy of fishing intensity. Furthermore, we modified this proxy with a smoothing function in order to ‘diffuse’ the signal around the actual event.
Results
The following maps present the values of \(E_{ij}\) for fisheries (grey = low exposure; dark blue = high exposure).
TrapFish
TrawFish
NetFish
DredFish
2.2. Cumulative exposure index
Here, we combine individual exposure indices into a unique value, the cumulative exposure index \(CE_{i}\), here with an additive relationship:
\[ CE_{i} = \sum_{j} E_{ij} \]
In future iterations, we will try different link functions to account for non-additive effects. This score varies between 0 and 15 (total number of considered human activities).
The cumulative exposure index has been represented in five classes, according to the colour code of the Marine Strategy Framework Directive (indigo = low exposure, less than 20 %; crimson = high exposure, higher than 80 %).
This histogram represents the number of stations falling in each class:
These scores will be used for the species distribution models (see section 2).